Optical resonance surface sensors are utilized in a number of chemical, pharmacological, and biotechnology research fields, including proteomics and drug discovery. Quantitation of surface-binding optical resonance profiles, such as Surface Plasmon Resonance (SPR) profiles, allows real-time observation and analysis of molecular interactions, providing data uninfluenced by biochemical labeling. As a consequence, optical resonance surface sensors have become widely used for the characterization of biological surfaces and the real-time monitoring of binding events.
At the present time, the most commonly used optical resonance surface sensors detect SPR. Surface plasmons are transverse electromagnetic charge-density waves that propagate parallel to the interface between a dielectric medium and a metallic film. Surface plasmons are generated by the interaction between the electron-rich surface of the metal and a charged particle or photon. Under appropriate conditions, the plasmons will resonate with light, resulting in the absorption of light.
More specifically, at an interface between two transparent media of different refractive index, light coming from the side having higher refractive index is partly reflected and partly refracted. Above a certain angle of incidence, no light is refracted across the interface and total internal reflection (TIR) is observed. While incident light is totally reflected, the electromagnetic field component does penetrate a short distance, on the order of tens or hundreds of nanometers, into a medium of lower refractive index, thus creating an exponentially detenuating evanescent wave. If the interface between the media is coated with a thin layer of metal, and the incident light is monochromatic and p-polarized, the intensity of the reflected light is reduced at a specific incident angle. This produces surface plasmon resonance due to the resonance energy transfer between the evanescent wave and the surface plasmons.
Many SPR sensors utilize the Kretschmann or Otto configurations, wherein the evanescent wave from totally internally reflected monochromatic light traveling through a prism creates a surface plasmon in a metal film that is in contact with the material to be detected. In these configurations, the light is incident on the metal film through the prism at an angle greater than a critical angle, known as the resonant angle θSPR. The surface plasmon is then detected by adjusting the angle of incidence until a sharp decrease in the reflected intensity is detected. If the permittivity or thickness of the dielectric layer changes, the resonant angle also changes.
In another common SPR configuration, the light is incident from the sample side of the metal film and is coupled to the surface to create the plasmon resonance by means of a diffraction grating in the metal surface. In still another SPR configuration, the metal film is deposited on the outside of an optical fiber or other waveguide and light is coupled into and out of the surface through the waveguide.
The existence of the SPR is detected by measurement of the intensity of the reflected light from the dielectric/metal interface, either from the back side (Kretschmann case) or the sample side (Otto and grating coupled cases). The resonance condition is sensitive to the effective refractive index of the medium adjacent to the metal film, and hence to the configuration of its surface. The term effective refractive index is used here because, if there is also a very thin (<<1 μm) solid biolayer in addition to the bulk fluid layer, then the biolayer will change the SPR angle and therefore cause the appearance of a change in the fluid refractive index. This is the common case, where both the biofilm and the bulk fluid refractive index affect the signal. Essentially, everything in the evanescent layer a few hundred nanometers thick has an influence. The surface configuration is therefore also changed by any material adsorbed onto the metal film, so that the binding of biomolecules to the film results in a change of the effective refractive index of the dielectric. Because of this, adsorption of molecules on the metallic film or conformational changes in the adsorbed molecules can be accurately detected. SPR imaging can therefore be used to detect the presence and/or amount of a biopolymer on a chemically modified metal surface by quantitation of the change in the local index of refraction that occurs upon adsorption.
For monochromatic or quasi-monochromatic illumination, the SPR angle will change directly according to the amount of bound materials; there is a linear relationship between the amount and the observed shift of the resonant angle. In particular, a linear relationship has been established between resonance angle and the mass concentration of biochemically relevant molecules such as proteins, sugars, and DNA. An SPR signal expressed in terms of angle shifts, or other units proportional to such shifts, is therefore a measure of mass concentration at the sensor chip surface. This means that analyte and ligand association and disassociation can be observed and rate and equilibrium constants may be calculated.
In an alternative SPR configuration, a fixed angle of incidence is employed and the wavelength of the exciting light is varied, or a broadband optical source is employed together with an array spectrometer. With this approach, the SPR appears as a dip in the reflected intensity as a function of wavelength, with the wavelength of the SPR minimum varying linearly as a function of mass concentration at the chip surface. This configuration can be employed with any of the coupling mechanisms previously described (prism, grating, or waveguide).
Surface plasmon resonance instruments may measure mass loading at a single spot, at several spots, or simultaneously at a large array of spots on an experimental surface (chip). In the case of an array instrument, the individual zones within which SPR shifts are measured are called Regions of Interest (ROIs).
The output of an SPR apparatus, whether the independent variable is angle or wavelength, is typically a graphed resonance curve. The location of the SPR resonance indicates the effective refractive index of the material on the sensor. Several approaches to SPR resonance curve shift quantitation have previously been utilized including, but not limited to:
(1) 1st moment below a baseline
(2) point of specific reflectance/signal
(3) polynomial fit about the minimum
(4) zero-crossing of the first derivative
(5) reflectance/signal at a specific point
(6) nonlinear fits of analytic functions
Some literature distinguishes between Absolute Refractive Index (RI) measurements and Relative RI measurements. The basis of this distinction is not entirely clear, since any precise absolute measurements must involve comparison with an RI standard. It is true, however, that, if a system is to be calibrated once and then used over time for absolute RI measurements, some algorithms are more suitable than others. This is due, for example, to such things as reduced sensitivity to sensor fouling or to baseline shifts. There also may be occasions where only changes in the refractive index are of interest. The same considerations apply, albeit to a reduced degree, to relative RI measurements of the sort required for measuring binding curves.
The position of the SPR curve minimum is the most common indicator of the absolute refractive index. The polynomial fit about the minimum (method (3)) and zero-crossing of the first derivative (method (4)) methods specifically determine this position. The other methods look at other aspects of the SPR curve in order to determine the minimum. Advantages of measuring absolute RI are that it looks at the SPR curve minimum, the measurement is insensitive to vertical shifts of the SPR curve (along the SPR signal axis), and the measurement is insensitive to fouling of the SPR sensor surface (which degrades the smoothness of the SPR curve). Disadvantages include that the measurement can be sensitive to the choice of points included in the analysis, potentially leading to distortion of the readings due to noise.
Prior to performing any of the analysis methods, it is possible to smooth the SPR curve. This can lead to reduced noise when tracking refractive index versus time. One common smoothing algorithm is a least-squares smooth, which typically incorporates from 1 to 12 points on either side of a point when determining the smoothed value of that point. Since smoothing does effectively bring multiple data points to bear on each smoothed point, algorithms which nominally depend on only one or a small number of data points may possibly be helped by smoothing procedures. In most cases, however, smoothing offers little or no benefit in well-designed fitting procedures, and can even hurt.
(1) 1st Moment Below a Baseline Method
The first moment method calculates the first moment of the SPR curve below a baseline. That is, only those parts of the SPR curve that are below the baseline are included in the calculation. For the simple case of n equally spaced data points, the algorithm may be expressed as:
      1    ⁢    st    ⁢                  ⁢    moment    =                    ∑                  i          =          1                n            ⁢                                                            SPRsignal              i                        -            Baseline                                    *        i                            ∑                  i          =          1                n            ⁢                                            SPRsignal            i                    -          Baseline                            where the summations exclude all data points where the SPR signal is greater than the baseline.
As long as the curve doesn't vertically shift, the algorithm will accurately track changes in the refractive index. Choosing where to set the baseline is not obvious. Frequently, the baseline is set at the midpoint of the SPR dip. Lowering the baseline will include fewer points in the analysis and may lead to increased noise. Raising the baseline includes more points, but the resulting calculation will deviate even more from the curve minimum. If the points selected for the analysis begin to shift out of the sensor range, the analysis will be degraded. There also may be times when an anomaly appears in the SPR curve, perhaps due to sensor surface fouling. It is still possible to use the sensor, so long as the anomaly is not near the SPR dip. To deal with this situation, various regions may be selectively excluded from the analysis. Thus, even if the anomaly is below the baseline, an accurate measurement results because the anomaly is excluded from the calculation.
This technique can exhibit good performance with respect to shot noise or other similar random additive noises, in part because it involves a large number of points and a very simple algorithm. A helpful addition is the provision of interpolation calculations at the baseline cutoff levels on either wing to handle the fact that baselines will rarely pass directly through data points. Smoothing of these cutoff zones can also be helpful. However, the fundamental disadvantage of the 1st moment technique for SPR is its high sensitivity to intensity or signal baseline shifts (vertical shifts of the SPR curve) due to the inherent asymmetry of SPR resonances. High data point density is therefore required. This method also tends to be sensitive to sensor surface fouling.
(2) Point of Specific Reflectance/Signal
The point of specific reflectance/signal method utilizes the pixel position at which the SPR curve is a pre-specified value. The curve is initially examined in order to approximately locate the data point where the curve is closest to the specified value. An nth order polynomial least squares fit is then performed in order to interpolate and identify exactly where on the curve the value occurs. The search may be done from either the left or the right side of the curve. As the SPR curve shifts along the x-axis, the identified point will follow this shift.
This method is susceptible to alterations in the overall shape of the SPR curve and it does not directly determine the minimum point. Still, it is useful for quantitating small shifts. In addition, it can be utilized to expand the dynamic range of the sensor. For example, if the minimum of the SPR curve is below pixel #1 (off the left side of the sensor range) the sensor may still be employed to track some other point on the SPR curve.
This technique has little to recommend it except simplicity. It suffers from much greater sensitivity to intensity or baseline changes than method (1), as well as being very sensitive to small changes in resonance shape. It uses very little of the resonance curve data for each determination, and thus has poor noise transfer performance. For decent performance, data point spacing must be tight.
Another version of this technique is to perform the calculation on both sides of the resonance and use the mean of the two to track the resonance. This is then similar to method (1), but with poorer noise performance since, again, only a relatively small subset of the data is used. It also has greater sensitivity than method (1) to intensity shifts.
(3) Polynomial Fit About the Minimum
In the polynomial fit about the minimum method, a first pass of the SPR curve is made in order to find the approximate location of the minimum of the resonance. An nth order polynomial least squares fit (using some number of points about the minimum) is then performed in order to interpolate the position of the minimum. This method is suitable for absolute refractive index measurements. This method is not susceptible to y-axis shifting of the SPR curve. However, since it only uses a relatively small number of points on the curve, it can be susceptible to the selection of points to be included in the calculation. This can sometimes lead to occasional anomalies in the analysis results (noise).
This method works fairly well, especially with respect to intensity and baseline shifts, but depends on relatively little data and so exhibits sub-optimal noise transfer performance. As with any method that actually attempts to locate the minimum of the resonance (as opposed to its overall position), it can be sensitive to noise near the bottom. Higher order polynomials, which can better fit the shape of the resonance, allow a wider range of data points to be included, but also offer more opportunity to move the minimum around to accommodate noise on individual data points. In other words, higher order polynomials have excess degrees of freedom that translate into increased noise injection into the shift determination. In practice, tight data point spacing is required, but the needed angle scan range can be fairly limited.
(4) Zero-Crossing of the First Derivative
The zero-crossing of the first derivative method is derived from the fact that the first derivative changes sign about the minimum of the SPR curve. In the zero-crossing algorithm, the approximate minimum point of the SPR curve is initially determined, a linear least-squares fit of the first derivative is performed using a few points about the approximate minimum, and the zero-crossing point is interpolated.
This amounts to a more or less direct determination of the actual minimum of the resonance curve, which is perhaps the least well-defined point on the curve. Many algorithms can be used to estimate the derivative and to find its zero crossing, and most of these do include some inherent smoothing or multi-point fitting, so that mathematically this process can be equivalent, for example, to method (3) (polynomial fit about the minimum). Using Savitsky-Golay derivatives, for example, the process is fully equivalent to method (3). Depending on the detailed implementation, this method can perform as well as method (3), and has much the same advantages and disadvantages. Poorly implemented, it can exhibit very poor noise performance. Again, tight data point spacing is needed. This method is suitable for making absolute refractive index measurements.
(5) Reflectance at a Specific Point
The reflectance/signal at a specific point method does not follow shifts of the SPR curve. It merely looks at the value of the SPR curve at a particular angle (or wavelength) position. If necessary, an nth order polynomial least squares fit is performed in order to interpolate the signal value at the desired Specific Point. This technique has often been used in the academic literature, since it can be utilized in a system without either moving parts or an array detector. It depends on the linearity of the side-wall of a resonance over a modest range of SPR shifts. It is essentially equivalent to method (2) (point of specific reflectance/signal) for small shifts, but, unlike method (2), it cannot accommodate larger shifts. One described implementation uses array detector information in which several data points surrounding the Specific Point are fitted, thereby somewhat improving the noise performance.
(6) Nonlinear Fits of Analytic Functions
Theoretical Responses. It has been common in the academic literature of SPR sensors to compare measured angular response curves with theoretical responses, and in some cases fits to these theoretical curves have been performed as a means of measuring film thicknesses, which amounts to measuring resonance shifts.
A paper from Wolfgang Knoll's laboratory in Mainz [M. Zizlsperger and Wolfgang Knoll, “Multispot parallel on-line monitoring of interfacial binding reactions by surface plasmon microscopy”, Progr. Colloid Polym. Sci., 109: 244-253 (1998)] shows diagrams (FIGS. 2 and 5) which appear to represent fits of experimental SPR angle response curves to simple Fresnel multilayer theory. The fits are fairly poor, but would suffice to measure resonance shifts. There is no discussion of the fitting method. Possible methods include manual trial and error parameter adjustment, or non-linear methods such as Levenberg-Marquardt.
A paper on Grating SPR sensors [C. R. Lawrence, N. J. Geddes, D. N. Furlong, J. R. Sambles, “Surface Plasmon resonance studies of immunoreactions utilizing disposable diffraction gratings”, Biosensors & Bioelectronics, 11: 389-400 (1998)] shows fits of experimental data to GSPR theory using a coupled wave method [J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region”, JOSA, 72: 839-846 (1982)]. The fitting procedure is not described, but could be a conventional non-linear least squares fit. It is stated that the fit involves a large number of parameters, including the optical constants of gold, the pitch and groove depth of the grating, and a groove distortion factor, as well as the thickness and (sometimes) the optical properties of an adsorbed protein layer. In some cases, certain of these parameters may be fixed. The fits are very good, indicating that great care was taken experimentally to avoid distortions and artifacts.
These techniques are in principle capable of very good results for SPR shift quantitation, provided that the number of free parameters is kept small. In other words, if a preliminary fit were used to establish all of the parameters except for the adlayer thickness, and subsequent run-time fits left only the thickness and a couple of amplitude scaling parameters free, then performance should be reasonably good.
Some downsides to this approach are:
a) The model calculations are very complex and intensive, particularly for the GSPR case.
b) Nonlinear fits themselves are very compute intensive (beyond the necessary theoretical model evaluations embedded therein), and exhibit instabilities that complicate automated operation.
c) In practice, frequent deviations of resonance shapes from the theoretical ideal are observed. Indeed, the data of Zizlsperger et al. show rather poor fits.
Explicit Functions. Yet another approach that has been suggested is non-linear fitting of relatively tractable explicitly defined mathematical functions to the run-time data. Unlike the Theoretical Responses, which are numerical profiles resulting from a complex computational process for a given set of input parameters, such explicit functions could be computed cheaply and are therefore much more attractive. In a way, this is an extension of the polynomial fitting approach, although polynomials have the property of allowing fast linear least squares fits.
If functional forms could be identified that have the flexibility to fit well to the range of observed profile shapes, this approach can work well. The downsides are:
a) The difficulty of identifying such functional forms, unless we restrict the fits to a small region around the minimum, in which case see Polynomial Fits, above. As a corollary, the difficulties of ensuring that future oddities in profile shapes that are not modelable by the chosen functional form do not occur.
b) The need, in general, for non-linear least squares or other non-linear fitting procedures.
c) Degraded noise performance due to the extra shape parameters likely needed to represent the full range of observed profiles. This problem can be sidestepped by the approach suggested above, in which a preliminary fit is used to fix most of the free parameters, leaving only resonance shift and amplitude(s) as fitting parameters.
Although most of the foregoing discussion has been about the most commonly utilized form of surface-binding optical resonance, SPR, optical resonance curves obtained from other types of surface-binding optical resonances are quantitated in a similar fashion. Examples of devices and techniques for measuring such resonances include optical waveguide sensors (such as the BIOS-1 angle scanned grating coupled optical waveguide instrument currently made by Artificial Sensing Instruments AG), grating couplers (K. Tiefenthaler (1993) “Grating couplers as label-free biochemical waveguide sensors”, Biosensors Bioelectron., 8:xxxv-xxxvii), plasmon waveguide resonance devices (Z. Salamon, H. A. Macleod and G. Tollin (1997) “Coupled Plasmon-Waveguide Resonators: A New Spectroscopic Tool of Probing Film Structure and Properties”, Biophysical Journal, 73:2791-2797), diffraction anomaly sensors (U.S. Pat. No. 5,925,878, Challener, 2000, “Diffraction anomaly sensor having grating coated with protective dielectric layer”), resonant mirror devices (R. Cush et al. (1993) “The Resonant Mirror: a Novel Optical Biosensor for Direct Sensing of Biomolecular Interactions”, Biosensors & Bioelectronics 8(7/8): 347-353), long range SPR (http://plazmon.ure.cas.cz/tobiska/optsen01.pdf), and the Perkin Elmer optical resonance analysis system described in WO 99/30135 (Tracy et al., published Jun. 17, 1999). To some extent, these devices and techniques are variations on two themes—dielectric planar waveguides and metal film SPR, or combinations thereof. All require no fluorescent label and are often called biosensors, but they are not restricted in their application to characterization of biofilms.
What has been needed, therefore, is a way to quantitate surface-binding optical resonance curves that requires low computational complexity and a minimal number of scan data points while still providing accurate determination of the resonance angle and good noise performance. This ability will in turn allow for longer scan times and/or scans over a greater number of ROIs, enhancing the utility of optical resonance surface sensor techniques for the observation of, for example, such phenomena as adsorption onto chemically modified metal surfaces, binding events involving biological molecules such as DNA, proteins, enzymes, and antibodies, and immunologic phenomena such as antigen-antibody reactions and antigen stimulation of tissue.